How can I make these eyelashes 'folllow' or 'pull' the verticies of the head object?
You should be able to do this by hooking the vertices of the eyelid to the eyelashes, so that the eyelash pulls them down, (which is what I think you are trying to do).

1) Select the portion of the eyelid you want to pull down, and create a vertex group for it in the vertex panel. 

2) Select the eyelashes that will affect the eyelid, then select the main mesh (in this case, the body, if that is the mesh that the eyelid is part of). 

3) With those two objects selected, press Ctrl+H, making sure you only have the part of the eyelid you want affected selected, and no other vertices.

4) Now you will notice that the eyelashes actually pull the vertices of the eyelid down with it when it moves, but it is probably going to look bad at first.

5) Select the main mesh, and go to the modifiers tab. Here you will see a modifier automatically added for the hooking object. You can adjust both the falloff type, radius, and the strength of the hook. This is for automatically adjusting the hook's influence proportionally. You also should select the vertex group you created earlier. This is for easy adjustment of the hook's influence. Using the settings in the modifier tab for the hook, adjust the strength and falloff until you get a value that nicely moves the eyelid. 

Note: This method works best with an object that has not had any subdivision modifiers applied yet, because the adjustments will be much smoother.

Hope this helps!